\section{Insurer Risk and Surplus Requirements}
\label{sec:SurplusRequirements}

I have shown that small insurers have higher probabilities, of high operating losses, than large insurers, a result capitation advocates must have failed to consider because this alone shows that capitation would never work in efficient health care (finance) systems. 

All insurers must anticipate years in which their PLREs exceed 0.8500. If they incur PLREs higher than 0.8500 and have no additional assets (Surplus\index{Surplus}), beyond current premiums, they become insolvent (bankrupt). Insolvency means failed commitments to suppliers, employees, stockholders, claimants, and policyholders. Regulators set many solvency requirements, including: minimum capitalization, statutory surplus and reserve requirements; rate regulation; restrictions on risky investments; and also conduct periodic financial inspections to reduce the numbers of insurer insolvencies (Barth, 2000; Cummins, Harrington and Niehaus, 1994).

\subsection{Solvency Preserving Loss Ratio}
\label{sec:SolvencyPreservingLossRatio}

There are no magic formulas for solvency protection. I require all insurers to meet a uniform solvency protection standard, the ``Solvency Preserving Loss Ratio\index{Solvency Preserving Loss Ratio}'' ($SPLR_N$\index{SPLR}). $SPLR_N$\index{$SPLR_N$} is the highest level PLRE insurers must be able to cover, before issuing policies, and it protects each insurer from PLREs up to PLR + 3 * $\sigma_{e_{I}}$, or all the Claims Costs it incurs with probability 0.9987. Insurers with adequate Surplus face insolvency less than 14 out of 10,000 years. 

Table~\ref{tab:InsurerOperatingResultsByPortfolioSize} Row 8, shows insurers' Solvency Preserving Loss Ratios. $SPLR_{PI}$ = 0.9000, but larger insurers, with lower standard errors, have lower SPLRs: $SPLR_{NHI} = 0.75855$ and  $SPLR_{B} = 0.79743$, while smaller insurers, with higher standard errors, have much higher SPLRs: $SPLR_{D} = 1.22434$ and $SPLR_{E} = 2.25000$. To be as well prepared as $PI$, to cover unusually high Claims Costs, $D$ and $E$ will need to idle huge amounts of Surplus, before issuing any policies. My risk adjusted Surplus requirement inhibits market entry by small, inefficient insurers, that are likely to fail, and encourages market entry by large, efficient insurers that are likely to succeed.

Regulators encourage other insurers to cover failed insurer's policies to maintain consumer confidence. $NHI$ and $B$, with profits over 9\%, and 5\%, can cover many failed insurers' policies and earn good will. But small, inefficient insurers decrease the  efficiency of insurance markets, taking excessive profits, or shifting their losses, to other insurers. 

\subsection{Surplus Requirements by Portfolio Size}
\label{sec:SurplusRequirementsByPortfolioSize}

Insurer's Surplus\index{Surplus} requirements, \textbf{${S_N}$}\index{$S_N$}, are dollar amounts of highly liquid assets, set aside before issuing policies, to cover the layer of operating losses between PLREs of 0.8500 and $SPLR_{N}$ [i.e. $S_{N}$ = Max(0,($SPLR_{N}$ - 0.8500) * Earned Premiums * Size)].  Table~\ref{tab:InsurerOperatingResultsByPortfolioSize} Row 9 shows that $S_{NHI}$ = $S_{B}$ = \$0.00 because $\Phi_{NHI}$(0.8500) = $\Phi_{B}$(0.8500) = 1.0000. $S_{PI}$ = \$200,000,000 at $SPLR_{PI}$ = 0.9000, $S_{D}$ = \$149,736,660 and $S_{E}$ = \$56,000,000 because $SPLR_{D}$ = 1.22434 and $SPLR_{D}$ = 2.2500. 

\subsection{Aggregate Surplus by Portfolio Size}
\label{sec:AggregateSurplusByPortfolioSize}

We want to insure all Americans so Table~\ref{tab:InsurerOperatingResultsByPortfolioSize} Row 10 shows, the total Surplus needs, in Billions of dollars, by portfolio size. $NHI$ and $B$ can insure everyone with \$0.00 aggregate Surplus, while 308 $PI$'s need \$61.6 Billion. But, 3,080 $D$'s need \$4.6 Trillion, and 30,800 $E$'s need \$172 Trillion. By ignoring small insurers', and risk assuming health care providers' Surplus needs, capitation advocates missed the greatest flaw in capitation, small insurers (risk assuming health care providers) need Trillions of dollars in Surplus. Inadequately capitalized, risk assuming health care providers have been failing, clinically and financially for decades (Mayes, 2005). In the aftermath of Hurricane Katrina, patients died because health care facilities were inadequately staffed and provisioned and could not continue to deliver care, despite having been paid, in advance, through capitation.

Before becoming health insurers, risk assuming health care providers should have diverted most of their assets to capitalizing their inefficient insurance operations, becoming inefficient clinicians because Surplus assets are not available to produce clinical services. Capitated providers continue their inefficient and under-capitalized insurance operations because capitation advocates refuse to admit that capitation cannot work in efficient health care (finance) systems.

While daunting, these aggregate Surplus levels are understated because $S_{N}$ protects single insurers. Bonferroni corrected aggregate surplus requirements for small insurers and risk assuming health care providers are much higher.
%Risk assuming health care providers cannot possibly set aside sufficient surplus to meet their exposure to higher than average levels of demand for health care services that may occur during epidemics, natural catastrophes, or (wo)man-made disasters. If risk assuming health care providers do set aside sufficient surplus for their insurance risks, they become inefficient clinicians. If they fail to set aside sufficient surplus, they are highly likely to fail to meet the needs of their patients. Portfolio size adjusted surplus requirements pose a significant barrier to entry into the insurance business for small insurers, and insurmountable barriers to entry into the insurance business for health care providers. 